1. In a large bowl, marinate the chicken pieces with red wine, garlic, thyme, salt, and pepper for at least 2 hours or preferably overnight.

2. In a large skillet, heat some oil and butter over medium-high heat. Add the marinated chicken pieces and brown them on all sides. Remove them from the skillet and set aside.

3. In the same skillet, add more butter and sauté onions, carrots, and mushrooms until they are soft. Sprinkle flour over the vegetables and stir well.

4. Return the chicken pieces to the skillet. Pour in the red wine marinade and chicken broth. Add garlic, bay leaf, and thyme. Cover and let it simmer for about 1 hour.

5. Serve the Coq au Vin hot, garnished with fresh parsley. It pairs well with crusty bread or mashed potatoes.